Mapping groundwater potential field using catastrophe fuzzy membership functions and Jenks optimization method: a case study of Maragheh-Bonab plain, Iran

Groundwater potential fields may be modeled by appropriate hydraulic equations governing aquifers, but these require a large amount of data not often available and subject to uncertainty. This paper approaches relative groundwater potential fields by integrating information derived from 11 data layers representing different distributed properties, but the emerging relativistic capability on deriving potential fields is not identical to hydraulics based one. Each of data layers has partial information and compared with one another, the layers are not homogeneous and not directly amenable to integration. One framework in the state-of-the-art of such problems is to use a catastrophe fuzzy membership function to capture and integrate the inherent information, but the decisions on the type of catastrophe function and the fuzzy-like membership intervals employ expert judgment. The paper builds on existing methodology to overcome this shortfall by the iterative identification of the type of catastrophe and using the Jenks optimization method to identify the break points in the data. The results project a new capability, according to which non-dimensional groundwater potential fields are an outcome of different catastrophes. For instance, in the study of non-dimensional groundwater potential fields of the aquifer along Sufichay (the River Sufi), the potential field combines contributions from two cusp catastrophes, one swallowtail catastrophe, two butterfly catastrophes and six wigwam catastrophes. The results provide anecdotal, but significant, evidence that the estimated potential field is fit for purpose.